On Queues with Interruptions and Repeat or Resumption of Service

This thesis entitled' On Queues with Interruptions and Repeat or Resumption of Service' introduces several new concepts into queues with service interruption. It is divided into Seven chapters including an introductory chapter. The following are keywords that we use in this thesis: Phase type (PH) distribution, Markovian Arrival Process (MAP), Geometric Distribution, Service Interruption, First in First out (FIFO), threshold random variable and Super threshold random variable. In the second chapter we introduce a new concept called the 'threshold random variable' which competes with interruption time to decide whether to repeat or resume the interrupted service after removal of interruptions. This notion generalizes the work reported so far in queues with service interruptions. In chapter 3 we introduce the concept of what is called 'Super threshold clock' (a random variable) which keeps track of the total interruption time of a customer during his service except when it is realized before completion of interruption in some cases to be discussed in this thesis and in other cases it exactly measures the duration of all interruptions put together. The Super threshold clock is OIl whenever the service is interrupted and is deactivated when service is rendered. Throughout this thesis the first in first out service discipline is followed except for priority queues.

Impact of Self-generation of Priorities and Non-preemptive Service in Single/Multiserver Queues

In this thesis we have studied a few models involving self-generation of priorities. Priority queues have been extensively discussed in literature. However, these are situations involving priority assigned to (or possessed by) customers at the time of their arrival. Nevertheless, customers generating into priority is a common phenomena. Such situations especially arise at a physicians clinic, aircrafts hovering over airport running out of fuel but waiting for clearance to land and in several communication systems. Quantification of these are very little seen in literature except for those cited in some of the work indicated in the introduction. Our attempt is to quantify a few of such problems. In doing so, we have also generalized the classical priority queues by introducing priority generation ( going to higher priorities and during waiting). Systematically we have proceeded from single server queue to multi server queue. We also introduced customers with repeated attempts (retrial) generating priorities. All models that were analyzed in this thesis involve nonpreemptive service. Since the models are not analytically tractable, a large number of numerical illustrations were produced in each chapter to get a feel about the working of the systems.

Faster Algorithms for Incremental Topological Ordering.Robert Tarjan

We present two online algorithms for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm takes O(m 1/2) amortized time per arc and our second algorithm takes O(n 2.5/m) amortized time per arc, where n is the number of vertices and m is the total number of arcs. For sparse graphs, our O(m 1/2) bound improves the best previous bound by a factor of logn and is tight to within a constant factor for a natural class of algorithms that includes all the existing ones. Our main insight is that the two-way search method of previous algorithms does not require an ordered search, but can be more general, allowing us to avoid the use of heaps (priority queues). Instead, the deterministic version of our algorithm uses (approximate) median-finding; the randomized version of our algorithm uses uniform random sampling. For dense graphs, our O(n 2.5/m) bound improves the best previously published bound by a factor of n 1/4 and a recent bound obtained independently of our work by a factor of logn. Our main insight is that graph search is wasteful when the graph is dense and can be avoided by searching the topological order space instead. Our algorithms extend to the maintenance of strong components, in the same asymptotic time bounds.

Proposta de um algoritmo híbrido de agendamento de grants baseado na priorização de filas para gerenciamento de recursos em WDM-PONs

As Redes Ópticas Passivas (Passive Optical Networks - PONs) vêm experimentando um sólido crescimento nas últimas décadas por terem sido concebidas como uma excelente alternativa para a solução de um dos maiores problemas para as redes de telecomunicações: o gargalo nas redes de acesso. A próxima geração desta tecnologia, as chamadas Next Genaration PONs (NG-PON), surgem como consequência da evolução das tecnologias ópticas e oferecem suporte aos serviços de próxima geração, melhorando os parâmetros de desempenho das TDM-PONs e inclusive aumentando a área de cobertura destas redes. Esta expansão geográfica beneficia as empresas de telecomunicações que passam a focar seus esforços na simplificação de suas infra-estruturas através da unificação das redes metropolitanas, de acesso e de backhaul, reduzindo a quantidade de nós e, consequentemente, de custos operacionais e financeiros. Trata-se de uma significativa mudança no cenário das redes de acesso que passam a ter grandes distâncias entre as Optical Network Units (ONUs) e o Central Office (CO) e uma imensa variedade de serviços, tornando fundamental a presença de algoritmos de agendamento capazes de gerenciar todos os recursos compartilhados de forma eficiente, ao mesmo tempo que garantem controle e justeza na alocação dinâmica dos tráfegos upstream e downstream. É a partir deste contexto que esta dissertação tem como objetivo geral apresentar a proposta de um algoritmo híbrido de agendamento de grants baseado na priorização de filas (Hybrid Grant Scheduler based on Priority Queuing – HGSPQ), que além de gerenciar todos os recursos em WDM-PONs, busca oferecer eficiência e controle ao Optical Line Terminal (OLT) no agendamento dinâmico dos tráfegos. Os resultados apresentados foram extraídos de cenários desenvolvidos em ambiente de simulação computacional e se baseiam nas métricas de atraso e vazão para avaliação de seu desempenho. Também será avaliado como a quantidade de recursos no OLT interfere nestas métricas.

Packet scheduling for priority based transmission in energy harvesting sensors

In this paper, we determine packet scheduling policies for efficient power management in Energy Harvesting Sensors (EHS) which have to transmit packets of high and low priorities over a fading channel. We assume that incoming packets are stored in a buffer and the quality of service for a particular type of message is determined by the expected waiting time of packets of that type of message. The sensors are constrained to work with the energy that they garner from the environment. We derive transmit policies which minimize the sum of expected waiting times of the two types of messages, weighted by penalties. First, we show that for schemes with a constant rate of transmission, under a decoupling approximation, a form of truncated channel inversion is optimal. Using this result, we derive optimal solutions that minimize the weighted sum of the waiting times in the different queues.

Queues with retrial/self-generation of priorities /postponement of work and some related reliability problems

Application of Queueing theory in areas like Computer networking, ATM facilities, Telecommunications and to many other numerous situation made people study Queueing models extensively and it has become an ever expanding branch of applied probability. The thesis discusses Reliability of a ‘k-out-of-n system’ where the server also attends external customers when there are no failed components (main customers), under a retrial policy, which can be explained in detail. It explains the reliability of a ‘K-out-of-n-system’ where the server also attends external customers and studies a multi-server infinite capacity Queueing system where each customer arrives as ordinary but can generate into priority customer which waiting in the queue. The study gives details on a finite capacity multi-server queueing system with self-generation of priority customers and also on a single server infinite capacity retrial Queue where the customer in the orbit can generate into a priority customer and leaves the system if the server is already busy with a priority generated customer; else he is taken for service immediately. Arrival process is according to a MAP and service times follow MSP.

Queues with Customer Induced Interruption

In this thesis we have introduced and studied the notion of self interruption of service by customers. Service interruption in queueing systems have been extensively discussed in literature (see, Krishnamoorthy, Pramod and Chakravarthy [38]) for the most recent survey. So far all work reported deal with cases in which service interruptions are generated by sources other than customers. However, there are situations where interruptions are due to the customers rather than the system. Such situations are especially arise at doctors clinic, banks, reservation counter etc. Our attempt is to quantify a few of such problems. Systematically we have proceed from single server queue (in Chapter 2) to multi-server queues (Chapter 3). In Chapte 4, we have studied a very general multiserver queueing model with service interruption and protection of service phases. We also introduced customer interruption in a retrial setup (in Chapter 5). All models (from Chapter 2 to Chapter 4) that were analyzed involve 'non-preemptive priority' for interrupted customers where as in the model discussed in Chapter 5 interruption of service by customers is not encouraged. So the interrupted customers cannot access the server as long as there are primary customers in the system. In Chapter 5 we have obtained an explicit expression for the stability condition of the system. In all models analyzed in this thesis, we have assumed that no more than one interruption is allowed for a customer while in service. Since the models are not analytically tractable, a large number of numerical illustrations were given in each chapter it illustrate the working of the systems. We can extend the models discussed in this thesis to several directions. For example some of the models can be analyzed with both server induced and customer induced interruptions the results for which are not available till date. Another possible extension of work is to the case where there is no bound on the number of interruptions a customer is permitted to have before service completion. More complex is the case where a customer is permitted to have a nite number (K ≥ 2) of We can extend the models discussed in this thesis to several directions.

Congestion pricing by priority auction

This paper analyzes a communication network facing users with a continuous distribution of delay cost per unit time. Priority queueing is often used as a way to provide differential services for users with different delay sensitivities. Delay is a key dimension of network service quality, so priority is a valuable resource which is limited and should to be optimally allocated. We investigate the allocation of priority in queues via a simple bidding mechanism. In our mechanism, arriving users can decide not to enter the network at all or submit an announced delay sensitive value. User entering the network obtains priority over all users who make lower bids, and is charged by a payment function which is designed following an exclusion compensation principle. The payment function is proved to be incentive compatible, so the equilibrium bidding behavior leads to the implementation of "cµ-rule". Social warfare or revenue maximizing by appropriately setting the reserve payment is also analyzed.

Randomized Push-Out Mechanisms in Priority Queuing and their Probability Characteristics

2002 Mathematics Subject Classification: 60K25.

Listening, sharing understanding and facilitating consumer, family and community empowerment through a priority driven partnership in Far North Queensland

Objectives: This paper provides an example of a mental health research partnership underpinned by empowerment principles that seeks to foster strength among community organizations to support better outcomes for consumers, families and communities. It aims to raise awareness among researchers and service providers that empowerment approaches to assist communities to address mental health problems are not too difficult to be practical but require long-term commitment and appropriate support. Methods: A collaborative research strategy that has become known as the Priority Driven Research (PDR) Partnership emerged through literature review,consultations, Family Wellbeing Program delivery with community groups and activities in two discrete Indigenous communities. Progress to date on three of the four components of the strategy is described. Results: The following key needs were identified in a pilot study and are now being addressed in a research-based implementation phase: (i) gaining two-way understanding of perspectives on mental health and promoting universal awareness; (ii) supporting the empowerment of carers, families, consumers and at-risk groups through existing community organizations to gain greater understanding and control of their situation; (iii) developing pathways of care at the primary health centre level to enable support of social and emotional wellbeing as well as more integrated mental health care; (iv) accessing data to enable an ongoing process of analysis/sharing/planning and monitoring to inform future activity. Conclusion: One of the key learnings to emerge in this project so far is that empowerment through partnership becomes possible when there is a concerted effort to strengthen grassroots community organizations. These include social health teams and men’s and women’s groups that can engage local people in an action orientation. Key words: Aboriginal, empowerment, Indigenous, mental health.

NAPLAN, a high priority or . . . ? Statements about its purpose in Queensland schools

This paper reports on statements from Professional Development participants who were asked to comment on NAPLAN. The participants were involved in a project designed by the YuMi Deadly Centre (YDC) for implementation into 25 Queensland School to enhance the teaching and learning of mathematics to Aboriginal and Torres Strait Islander students and low SES students. Using an action research framework and a survey questionnaire, the preliminary data obtained from participating principals is mixed, with statements indicating that NAPLAN is a high priority for some schools while others indicated that it does not “tell” the whole story of student learning.